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Thread: parametrization and stokes's theorem

  1. #1
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    parametrization and stokes's theorem

    Let $\displaystyle F (x, y, z) = 6yx^2$i + $\displaystyle 2x^3$j + $\displaystyle 6xy$k, and $\displaystyle C$ be the curve of intersection of the hyperbolic paraboloid $\displaystyle z = y^2 - x^2$ and the cylinder $\displaystyle x^2 + y^2 = 25$ oriented counterclockwise as viewed from above.
    (i) Obtain a parametrization of the curve $\displaystyle C$ and use the result to evaluate $\displaystyle \int_{C} F \cdot d$r.
    (ii) use Stokes's Theorem to evaluate $\displaystyle \int_{C} F \cdot d$r.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    See the attachment.

    If you have trouble visualising the curve you can see the animation

    motion on a saddle on my web site Calculus 3
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